CANONICAL QUANTIZATION OF CYLINDRICALLY SYMMETRIC MODELS

TL;DR

This paper performs canonical quantization of cylindrically symmetric solutions, linking Levi-Civita and Kasner models, and predicts quantum effects on cosmic string geometries, including the wedge angle.

Contribution

It introduces a quantum model unifying Levi-Civita and Kasner spacetimes with non-fixed topology, and completes the quantization of cosmic string exterior solutions.

Findings

Quantum model relates Levi-Civita and Kasner solutions.

Predicts quantum effects on cosmic string wedge angle.

Establishes a unified phase space for cylindrical spacetimes.

Abstract

We carry out the canonical quantization of the Levi-Civit\`a family of static and cylindrical solutions. The reduced phase space of this family of metrics is proved to coincide with that corresponding to the Kasner model, including the associated symplectic structures, except for that the respective domains of definition of one of the phase space variables are not identical. Using this result, we are able to construct a quantum model that describes spacetimes of both the Levi-Civit\`a and the Kasner type, and in which the three-dimensional spatial topology is not uniquely fixed. Finally, we quantize to completion the subfamily of Levi-Civit\`a solutions which represent the exterior gravitational field of a straight cosmic string. These solutions are conical geometries,ie, Minkowski spacetime minus a wedge. The quantum theory obtained provides us with predictions about the angular size of this wedge.